Refraction error compensation modeling method and system for ground object detection

Abstract

The present invention relates to a ground object detection refraction error compensation modeling method and system, belonging to the field of earth remote sensing detection and space remote sensing technology. The atmosphere between an aircraft and the earth's surface is divided into N layers, and the distance between two adjacent layers is calculated. Then, according to Snell's law, the light refraction angle at each atmospheric layer is obtained. The Hopfield model of the atmospheric refractive index and the e-exponent joint model are combined to realize the simulation calculation of the atmospheric refractive index profile, and then the horizontal distance between two adjacent atmospheric layers on the light propagation path is obtained. Finally, the vertical distance from the aircraft to the earth's surface is combined to calculate the angle between the line connecting the aircraft and the true position of the ground object and the vertical line to the center of the earth, that is, the true elevation angle, so as to analyze and obtain the elevation angle error and distance error. The present invention can correct the elevation angle error and distance error of the aircraft caused by atmospheric refraction, and thus be applied to the accurate identification and positioning of the observed target.

Description

Technical Field

[0001] The present invention relates to a ground object detection refraction error compensation modeling method and system, belonging to the technical field of earth remote sensing detection and space remote sensing. Background Art

[0002] The density of the Earth's atmosphere is a continuous curve that varies with altitude. Refraction is caused by differences in the speed of light in different substances. Closer to the surface, the atmospheric density increases, slowing light propagation and increasing the refractive index. Further away from the surface, the atmospheric density decreases, accelerating light propagation and decreasing the refractive index. When observing ground objects from an aircraft, light traverses layers of atmosphere of varying density, causing it to bend due to refraction. This ultimately results in discrepancies between the observed position of the object and its actual location, impacting the detection and positioning of distant objects and the study of their shape and surface properties. This discrepancy is particularly pronounced during high-altitude observations (e.g., from satellites or high-altitude aircraft) or at high angles, severely limiting the reliability and application value of remote sensing data.

[0003] The problems of the prior art are as follows:

[0004] The hierarchical model lacks accuracy:

[0005] Traditional methods simplify the atmosphere into a finite number of layers (usually N = 1-200 layers) and calculate the refraction angle layer by layer using Snell's law. However, too few layers can lead to increased cumulative errors in the refraction path, resulting in large fluctuations in the calculated results and failing to meet the requirements of high-precision positioning.

[0006] Simplified refractive index model:

[0007] Existing methods use a single model (such as the Hopfield model or the e-exponential model) to describe the change in atmospheric refractivity with altitude. However, there are significant differences in the distribution patterns of atmospheric refractivity near the surface and in high altitude areas: the existing technology does not effectively combine the advantages of the two models, resulting in systematic deviations in the refractive index calculations across elevation areas. For example, the existing patent publication number CN118707452A discloses a method and device for correcting atmospheric refraction errors in low-dimensional areas. This method combines Snell's theorem and an iterative optimization algorithm to achieve error correction through integral operations and interpolation. Its core lies in improving the correction efficiency of low-dimensional areas (such as flat terrain) through layered segmentation, but it does not involve joint modeling of the entire elevation range.

[0008] Insufficient dynamic coupling of environmental parameters:

[0009] Existing methods do not fully consider the dynamic impact of real-time environmental parameters (such as temperature, pressure, and wavelength λ) at the location of the object on the refractive index, resulting in unreliable correction results. Summary of the Invention

[0010] The purpose of the present invention is to propose a modeling method and system for refraction error compensation in ground object detection. Based on information such as the direction of sight, flight altitude, and wavelength of an aircraft's view of the ground object being observed, an atmospheric refraction line-of-sight error compensation algorithm is established. During this construction process, the Hopfield model and the e-exponent model of atmospheric refractive index are combined to simulate the atmospheric refractive index profile. Finally, by calculating the difference between the aircraft's apparent elevation angle and its true elevation angle, an elevation error model is constructed to correct the aircraft's elevation error caused by atmospheric refraction, thereby enabling accurate identification and positioning of the observed target. This method solves the problems encountered in the prior art.

[0011] The ground object detection refraction error compensation modeling method of the present invention comprises the following steps:

[0012] S1: Divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers;

[0013] S2: Solve the angle of refraction of light at each atmospheric layer according to Snell's law;

[0014] S3: Calculate the horizontal distance between two adjacent atmospheric layers along the light propagation path;

[0015] S4: Based on the result of step S3, the distance between the projection of the aircraft on the ground surface and the true position of the ground object is calculated;

[0016] S5: combining the vertical distance from the aircraft to the earth's surface and the distance obtained in step S4, calculating the angle between the line connecting the aircraft and the true position of the ground object and the vertical line to the center of the earth, i.e., the true elevation angle;

[0017] S6: Calculate the elevation angle error and the distance error based on the actual elevation angle in step S5 and the angle between the line connecting the apparent position of the aircraft to the ground object and the vertical line to the center of the earth, that is, the apparent elevation angle.

[0018] Preferably, when the atmosphere is divided into N layers in step S1, the distance between two adjacent layers is ,in h is the distance from the aircraft to the Earth's surface.

[0019] Preferably, in step S2, the Earth's atmosphere is layered. Assuming that the atmospheric density is the same between the same layers and different between different layers, the Snell's law is satisfied between two adjacent layers. Similarly, the following relationship holds true:

[0020]

[0021] From this, the refraction angle of each layer can be calculated:

[0022]

[0023] in: is the refractive index of the 0th layer of atmosphere, is the incident angle of layer 0, is the refractive index of the first layer of atmosphere, is the refraction angle of the first layer, and so on. is the refractive index of the N-1th layer of atmosphere, is the incident angle of the N-1th layer, is the atmospheric refractive index of the Nth layer, is the refraction angle of the Nth layer; according to the interior alternate angle theorem, the calculated refraction angle is the incident angle of the next layer.

[0024] Preferably, the calculation of the atmospheric refractive index includes: The atmospheric refractive index at the apparent position of the ground object is expressed by the following formula:

[0025]

[0026] Where, , t, P, e a ,λ They refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the location of the feature respectively;

[0027] The atmospheric refractive index along the light propagation path is expressed by the following formula:

[0028]

[0029] in, Indicates elevation, by 40136+148.72× t Calculated, the unit is m, below the elevation, each altitude position The atmospheric refractive index at the altitude is given by the Hopfield model. Above the altitude, the altitude The atmospheric refractive index at e The exponential model is given by represents the atmospheric refractive index at the altitude, β is the piecewise fit index.

[0030] Preferably, the horizontal distance between two adjacent layers in step S3 is calculated using the following formula:

[0031] .

[0032] Preferably, in step 4, the distance between the projection of the aircraft on the ground and the true position of the ground object is calculated based on the result obtained in step 3. :

[0033]

[0034] Preferably, in step S6, the elevation angle error is calculated based on the actual elevation angle calculated in step S5, combined with the angle between the line connecting the apparent position of the aircraft and the ground object and the vertical line to the center of the earth, that is, the apparent elevation angle, and is expressed as:

[0035]

[0036] Among them, Z0 is the angle between the line connecting the aircraft and the ground object and the vertical line of the center of the earth, that is, the apparent elevation angle. This value is a known quantity. θ It is the angle between the line connecting the true position of the aircraft and the ground object and the vertical line to the center of the earth, that is, the true elevation angle, which is calculated in step S5.

[0037] Preferably, the distance error in step S6 represents the distance between the true position of the object and the apparent position of the object, expressed as It is expressed as follows:

[0038]

[0039] in, h is the distance from the aircraft to the surface of the earth, which is a known quantity. It is the distance from the projection of the aircraft on the surface of the earth to the true position of the object. Z0 is the angle between the line connecting the apparent position of the aircraft and the object and the vertical line to the center of the earth, that is, the apparent elevation angle.

[0040] The ground object detection refraction error compensation modeling system of the present invention comprises:

[0041] Layering module: used to divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers;

[0042] Refraction angle calculation module: Iteratively solves the refraction angle of each atmospheric layer based on Snell's law;

[0043] Horizontal distance calculation module: calculates the horizontal distance between adjacent layers based on the refraction angle and layer distance;

[0044] Projection distance module: accumulates the horizontal distances of all layers to obtain the distance from the projection of the aircraft on the surface to the true position of the ground object;

[0045] True elevation angle calculation module: combines the vertical distance of the aircraft and the projected distance to calculate the true elevation angle;

[0046] Error calculation module: Calculates the elevation angle error and distance error based on the difference between the true elevation angle and the apparent elevation angle.

[0047] Preferably, the value range of N in the layered module is 900 to 1000, and the distance between adjacent layers is fixed at 100 meters.

[0048] Compared with existing technologies, the present invention's ground object detection refraction error compensation modeling method and system can correct the aircraft's elevation angle error and distance error caused by atmospheric refraction, thereby being applied to the precise identification and positioning of observed targets. It has the following beneficial effects:

[0049] ① High-precision error correction: Combining the Hopfield model with the e-index segmented refractivity model, the optimal model is used in areas below the elevation (near the surface) and above the elevation (high altitude) to reduce the error in cross-layer refractivity calculation.

[0050] By optimizing the number of atmospheric layers to 900-1000 and fixing the layer spacing at 100 meters, the calculation efficiency and accuracy are effectively balanced, and the fluctuation of the elevation angle error is controlled within ±0.5 arc seconds.

[0051] ② Multi-band adaptability: By introducing the wavelength parameter λ to dynamically correct the refractive index calculation formula, it supports unified correction of multiple bands such as visible light, near-infrared, medium-wave infrared and long-wave infrared.

[0052] ③ Dynamic environmental parameter coupling: real-time temperature (t), pressure (P), water vapor pressure (e) at the integrated object location a ) and wavelength (λ) parameters to improve the adaptability of the model in extreme climates and complex geographical environments.

[0053] ④ Full altitude and global applicability: Covering the 40-120km altitude range and verifying its applicability in different geographical regions, the standard deviation of elevation error is less than 0.3 arc seconds, meeting global remote sensing monitoring needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of the ground object detection refraction error compensation modeling method according to Example 1 of the present invention;

[0055] Figure 2 Schematic diagram of observation geometry for the ground object detection refraction error compensation modeling method according to Example 1 of the present invention;

[0056] Figure 3 The corresponding relationship between the elevation angle error and the altitude within the range of 1-80 km in Example 1 of the present invention;

[0057] Figure 4 This is a schematic diagram of the observation of the variation of the elevation angle error within the range of 1-80 km at an apparent zenith distance of 45° in Example 1 of the present invention;

[0058] Figure 5 Graph showing the corresponding relationship between distance error and altitude in Example 1 of the present invention;

[0059] Figure 6This is a graph showing the corresponding relationship between the elevation angle error and the altitude under the condition of an apparent zenith distance of 45° in Example 1 of the present invention;

[0060] Figure 7 This is a comparison diagram of the results of the present invention and the existing SIDNEYBERTRAM in Example 1 of the present invention. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0062] Example 1:

[0063] like Figure 1-Figure 2 As shown, this embodiment discloses a ground object detection refraction error compensation modeling method, including the following steps:

[0064] Step 1: Divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers;

[0065] In step 1, the atmosphere between the aircraft and the ground is divided into N layers, and the distance between two adjacent layers is , h It is the distance from the aircraft to the surface of the earth. In theory, the larger the layer N, the better. However, too large N will lead to slow calculation speed. Through calculation, it is found that when N is relatively small (1-200), the calculation results have large fluctuations. When N is in the range of 900-1000, the calculation results fluctuate less. In order to ensure the accuracy of the calculation results and the calculation speed of the program, the distance between atmospheric layers is fixed at 100 meters. It has been verified that when the altitude resolution is 100 meters, the elevation angle error fluctuates less.

[0066] Step 2: Solve the Snell's law to obtain the angle of refraction of light at each atmospheric layer;

[0067] In step 2, based on the stratification results of the Earth's atmosphere in step 1, assuming that the atmospheric density is the same between the same layers and different between different layers, then the Snell's law is satisfied between two adjacent layers. For example, the refractive index of the 0th layer of atmosphere is , the angle of incidence is , the refractive index of the first layer of atmosphere is , the refraction angle is , then Snell's law can be used to obtain , according to the interior alternate angle theorem, the calculated refraction angle is the incident angle of the next layer, so for the first and second layers, there is a relationship , and so on, the following relationship holds:

[0068]

[0069] Thus, the refraction angle of each layer can be calculated.

[0070]

[0071] The solution of the atmospheric refractive index in step 2 is a key, which is related to the calculation of the refraction angle of each layer of atmosphere. It represents the atmospheric refractive index at the apparent position of the ground object, which can be expressed by the following formula:

[0072]

[0073] in, , t, P, e a ,λ They refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the location of the feature respectively;

[0074] The atmospheric refractive index along the light propagation path can be expressed by the following formula:

[0075]

[0076] in, Indicates elevation, which can be calculated by 40136+148.72× t Calculated, the unit is m, below the elevation, each altitude position The atmospheric refractive index at the altitude is given by the Hopfield model. Above the altitude, the altitude The atmospheric refractive index at e The exponential model is given by represents the atmospheric refractive index at the altitude, β is the piecewise fit index.

[0077] Step 3: Calculate the horizontal distance between two adjacent atmospheric layers along the light propagation path;

[0078] In step 3, the horizontal distance between two adjacent atmospheric layers on the light propagation path is calculated. The horizontal distance between two adjacent atmospheric layers can be expressed as:

[0079]

[0080] Step 4: Based on the result obtained in step 3, calculate the distance between the projection of the aircraft and the ground surface and the true position of the ground feature;

[0081] In step 4, the distance between the projection of the aircraft and the ground surface and the true position of the ground object is calculated based on the result obtained in step 3. :

[0082]

[0083] Step 5: Based on the conclusion of step 4 and the vertical distance from the aircraft to the earth's surface, calculate the angle between the line connecting the aircraft and the true position of the ground feature and the vertical line to the center of the earth, that is, the true elevation angle;

[0084] In step 5, based on the conclusion of step 4 and the vertical distance from the aircraft to the earth's surface, the angle between the line connecting the aircraft and the true position of the ground feature and the vertical line to the center of the earth is calculated, that is, the true elevation angle. The calculation formula is as follows:

[0085]

[0086] in, h is the distance from the aircraft to the surface of the earth, which is a known quantity. It is the distance from the projection of the aircraft on the earth's surface to the true position of the object.

[0087] Step 6: Based on the actual elevation angle calculated in step 5, the angle between the line connecting the aircraft and the apparent position of the ground object and the vertical line to the center of the earth, that is, the apparent elevation angle, is combined with the elevation angle error and the range error.

[0088] In step 6, the actual elevation angle calculated in step 5 is combined with the angle between the line connecting the aircraft and the apparent position of the ground object and the vertical line of the center of the earth, that is, the apparent elevation angle, to calculate the elevation angle error, which can be expressed as:

[0089]

[0090] Among them, Z0 is the angle between the line connecting the aircraft and the ground object and the vertical line of the center of the earth, that is, the apparent elevation angle. This value is a known quantity. θ It is the angle between the line connecting the true position of the aircraft and the ground object and the vertical line to the center of the earth, that is, the true elevation angle, which is calculated in step 5.

[0091] The distance error represents the distance between the true position of the object and the apparent position of the object, which is expressed as It is expressed as follows,

[0092]

[0093] in, h is the distance from the aircraft to the surface of the earth, which is a known quantity. It is the distance from the projection of the aircraft on the surface of the earth to the true position of the object. Z0 is the angle between the line connecting the apparent position of the aircraft and the object and the vertical line to the center of the earth, that is, the apparent elevation angle.

[0094] To verify the accuracy and reliability of the calculation results, the elevation angle error was calculated using the following environmental parameters: time (UTC): 2023-04-15; 12:00:00 PM, the aircraft was flying over Beijing, the solar activity index F107 was 60 sfu, the geomagnetic activity index Ap was 10 nT, the angle between the line connecting the aircraft's apparent position to the ground object and the vertical to the center of the Earth was between 0 and 30°, and the aircraft was flying at an altitude of 40 to 120 km. The elevation angle errors for the visible, near-infrared, medium-wave, and long-wave bands were calculated for deflections of 0 to 30° relative to the vertical to the center of the Earth and at altitudes of 40 to 120 km. These are shown in Tables 1, 2, 3, and 4, respectively. The units of the elevation angle errors are arc seconds.

[0095] Table 1 Elevation angle error (unit: arc seconds) in the visible light wavelength range 0.39~0.78μm (0.58μm is selected)

[0096]

[0097] Table 2 Elevation angle error in the near-infrared band 0.78-2.5μm (1.64μm selected)

[0098]

[0099] Table 3 Elevation angle error in the medium wave band 3-5μm (4μm selected)

[0100]

[0101] Table 4 Elevation angle error in the longwave band 8–14 μm (11 μm selected)

[0102]

[0103] Through the calculation results of Tables 1, 2, 3, and 4, it is found that the atmospheric refraction angle (elevation angle error) tends to decrease with the increase of wavelength. The calculation formula for the absolute refractive index is n=sini / sinr=c / v, where c is the speed of light in a vacuum and v is the speed in the medium. From v=λ*f, we know that in the same medium, the longer λ is, the larger v is. Since the speed of light c is a constant, it can be concluded that in the same medium, the longer λ is, the smaller the refractive index n is. Therefore, as the wavelength decreases, the refraction effect becomes more significant and the atmospheric refraction angle increases. However, as the wavelength increases, the atmospheric refraction angle gradually decreases.

[0104] The above calculations show that the atmospheric refraction angle increases with increasing observation angle. This is because as the observation angle increases, the distance light travels in the atmosphere increases. As the light travels longer, the refraction effect becomes more significant, leading to an increase in the atmospheric refraction angle. Furthermore, it was found that within the 40-120 km altitude range, the atmospheric refraction angle decreases with increasing altitude. To understand the relationship between the atmospheric refraction angle and altitude, the corresponding relationship between the atmospheric refraction angle and altitude was plotted for the 1-80 km range.

[0105] By calculating the variation of elevation angle error with altitude in the range of 1–80 km under the conditions of apparent zenith distance of 25°, 30°, 35°, and 45°, it is found that the elevation angle error first increases and then decreases with altitude, such as Figure 3 As shown, the elevation angle error is largest at an altitude of approximately 15 km.

[0106] Cause Analysis:

[0107] Taking the variation law of elevation angle error within the range of 1-80km at an apparent zenith distance of 45° as an example, Figure 4 is an observation diagram, S represents the distance from the aircraft to the apparent position of the ground object, γ represents the elevation error, h represents the altitude of the aircraft, △ Indicates the distance error between the true position of the object and the apparent position of the object, in order to show the elevation error γ The changing law between ΔH and flight height h requires the establishment of a relationship between the two. Based on the sine theorem, the following relationship is obtained:

[0108]

[0109] in , then the above formula can be converted to,

[0110]

[0111] Further simplifying the above formula, we can get:

[0112]

[0113] Thus we can get γ and h The relationship between

[0114]

[0115] In the above formula, △ Indicates difference h The distance error between the true position and the apparent position of the corresponding object has been calculated by the refraction compensation system. Figure 5For the condition of 45° apparent zenith distance and altitude range of 1-80km, △ and h The corresponding relationship diagram between them.

[0116] There is a complex inverse tangent relationship between the elevation error γ and the altitude h. Figure 6 The corresponding relationship between the elevation error γ and the height h under the condition of 45° apparent zenith distance is shown, because there is a formula between γ and h Such a relationship shows that the elevation angle error first increases and then decreases with increasing altitude.

[0117] The density of Earth's atmosphere is a continuous curve that varies with altitude. Refraction is caused by differences in the speed of light propagating through different substances. The closer to the surface, the greater the atmospheric density, the slower the light propagation speed, and the greater the refractive index. The farther from the surface, the less dense the atmosphere, the faster the light propagation speed, and the smaller the refractive index. When observing ground objects from an aircraft, light bends due to refraction as it passes through layers of atmosphere with varying densities. This ultimately results in discrepancies between the observed object's position and its actual location, impacting the detection and positioning of distant targets and the study of their shape and surface properties.

[0118] Accuracy verification experiment:

[0119] (1) Influence of water vapor pressure on elevation error

[0120] Although the atmospheric water vapor content is low, it does affect the refractive index, thus affecting elevation error. Water vapor pressure has a distinct latitudinal distribution, with a maximum of approximately 30 hPa at the equator and gradually decreasing toward the poles. The water vapor pressure on land surfaces varies between 0 and 30 hPa, with a higher value near the ground and then decreasing rapidly with increasing altitude. Assuming the vertical distribution of water vapor pressure is as shown below,

[0121]

[0122] in, is the surface water vapor pressure, Indicates the distance above the ground surface in km.

[0123] To analyze the effect of water vapor pressure on elevation error, the elevation error was calculated with and without water vapor pressure, and the difference between the two was calculated. The environmental parameters were: Beijing's longitude and latitude (39.56°, 116.20°), time (UTC, September 1, 2022), 12:00:00 PM, and wavelength (0.58 μm).

[0124] Calculate separately =30hPa and = 0, the elevation angle error (unit: arc seconds) of the aircraft at 40km, 70km, and 100km flight altitudes, and calculate the difference error between the two. The error is defined as = 0 under the condition of elevation error and =The difference in elevation angle error under the condition of 30hPa. The calculation results are shown in Tables 5, 6 and 7.

[0125] Table 5 Elevation angle error of the aircraft at a flight altitude of 40 km

[0126]

[0127] Table 6 Elevation angle error of the aircraft at a flight altitude of 70 km

[0128]

[0129] Table 7 Elevation angle error of the aircraft at a flight altitude of 100 km

[0130]

[0131] The above calculation results show that the effect of water vapor pressure on elevation angle error is within 10 -4 –10 -3 The influence of water vapor pressure on the elevation angle error accuracy is about 0.005%. Therefore, under normal weather conditions, the influence of water vapor pressure on the elevation angle error of ground refraction can be ignored.

[0132] In rainy, snowy, cloudy, overcast and other weather conditions with high water vapor, the land water vapor pressure can reach 45hPa. In order to analyze the changes in elevation angle error under severe weather conditions such as rainy, snowy, and overcast, the initial values ​​of water vapor pressure are calculated respectively. =35hPa, 40hPa, 45hPa, the aircraft's elevation angle error (unit: arc seconds) at 40km, 70km, and 100km flight altitudes, and the initial value of water vapor pressure = 0, and the calculation results are shown in Table 8.

[0133] Table 8 Effect of water vapor pressure on elevation angle error under extreme conditions

[0134]

[0135] From the table above, we can see that in rainy, snowy, cloudy and other weather conditions with high water vapor, the change in elevation angle error caused by water vapor pressure is within 5×10 -3 –5×10 -3 Within arc seconds, the maximum impact on the elevation angle error accuracy is about 0.0068%. Therefore, regardless of the weather conditions such as rain, snow, cloudy, overcast, or in general, the impact of water vapor pressure on the elevation angle error accuracy is very small.

[0136] By analyzing the general weather conditions ( ≤30hPa) and rain, snow, cloudy, overcast and other conditions with high water vapor ( Under the weather condition of ≤30hPa, the influence of water vapor pressure on the elevation angle error of ground objects is analyzed. It is found that the influence of water vapor pressure on the accuracy of elevation angle error is less than 0.0068%, which is an extremely small value. In summary, the influence of water vapor pressure on ground object refraction can be ignored.

[0137] (2) Effect of temperature on elevation error

[0138] The temperature of the Earth's atmosphere does not change uniformly. In the troposphere and mesosphere, the atmospheric temperature decreases with increasing altitude. In the troposphere, the temperature drops by about 6°C for every 1km increase in altitude. In the stratosphere, there will be an inversion layer, that is, the temperature increases with increasing altitude. In the thermosphere, the temperature also increases with increasing altitude. In order to analyze the influence of temperature on the elevation error, in actual operation, it is assumed that the pressure remains unchanged and the water vapor pressure e a =0, calculate the change of elevation angle error when the temperature changes ΔT.

[0139] Environmental parameters are: Beijing's longitude and latitude (39.56°, 116.20°), September 1, 2022, 12:00:00 PM (UTC), a solar activity index F107 of 60 sfu, a geomagnetic activity index Ap of 10 nT, and a wavelength of 0.58 μm. Based on these environmental parameters, the initial temperature and pressure values ​​at the feature location are calculated using the NRLMSIS2.0 model. These values ​​can also be obtained using other models or measured data.

[0140] Calculate the elevation angle error (unit: arc seconds) of the aircraft at 40km, 70km, and 100km flight altitudes under the conditions of temperature change ΔT (±1K, ±5K, ±10K), as shown in Tables 9, 10, and 11.

[0141] Table 9 Elevation angle error of aircraft with temperature change ΔT at 40km flight altitude

[0142]

[0143] Table 10 Elevation angle error of the aircraft at a flight altitude of 70 km due to temperature change ΔT

[0144]

[0145] Table 11 Elevation angle error due to temperature change ΔT at an aircraft altitude of 100 km

[0146]

[0147] Based on the elevation error values ​​due to ground object refraction in Tables 9, 10, and 11, the difference between the elevation error under conditions of ΔT changes of ±1K, ±5K, and ±10K and the elevation error under ΔT of zero is calculated. Here, we define error1 as the difference between the elevation error under conditions of ΔT changes of ±1K and ΔT of zero, error5 as the difference between the elevation error under conditions of ΔT changes of ±5K and ΔT of zero, and error10 as the difference between the elevation error under conditions of ΔT changes of ±10K and ΔT of zero. Table 12 shows the absolute values ​​of error1, error5, and error10 within the apparent elevation angle range of 5–30° at flight altitudes of 40km, 70km, and 100km, respectively.

[0148] Table 12 Absolute values ​​of error1, error5, and error10 within the apparent elevation angle range (unit: arc seconds)

[0149]

[0150] From Table 12, we can see that as the aircraft altitude increases, the change of the elevation angle error caused by temperature decreases. As the aircraft's viewing direction and the deflection angle relative to the vertical line of the earth's center increase, the change of the elevation angle error caused by temperature increases. For every 1K change in temperature, the elevation angle error changes by about 10 -3 –10 -2 In the order of arc seconds, the elevation error can change by 10 for every 10K change in temperature. -1 At the arc second level, calculations show that even if the temperature changes by 10K, the impact on the elevation angle error accuracy is still less than 5%.

[0151] (3) Effect of pressure on elevation error

[0152] Atmospheric pressure is the atmospheric pressure per unit area, numerically equal to the weight exerted on a vertical column of air extending upward from that unit area to the upper boundary of the atmosphere. The atmosphere is divided into different vertical layers, each with a different air pressure. At sea level, the air pressure is approximately 1013.25 hPa, but it decreases with increasing altitude. At an altitude of approximately 5.5 km, the air pressure is only about half that at sea level.

[0153] In order to analyze the influence of pressure on the elevation angle error, in actual operation, it is assumed that the temperature remains unchanged and the water vapor pressure e=0, and the change of the elevation angle error when the pressure changes ΔP is calculated respectively.

[0154] The elevation angle errors (unit: arc seconds) of the aircraft at flight altitudes of 40 km, 70 km, and 100 km are calculated for pressure changes ΔP (~1 hPa, ~5 hPa, ~10 hPa, and ~50 hPa), respectively, as shown in Tables 13, 14, and 15.

[0155] Table 13 Elevation error of pressure change ΔP at an aircraft altitude of 40 km

[0156]

[0157] Table 14 Elevation angle error of pressure change ΔP at an aircraft altitude of 70 km

[0158]

[0159] Table 15 Elevation error of pressure change ΔP at an aircraft altitude of 100 km

[0160]

[0161] From the elevation angle error values ​​in Tables 13, 14, and 15, calculate the elevation angle errors under the conditions of ΔP changes of 1‰, 5‰, 1%, and 5%, respectively (where a ΔP change of 1‰ is equivalent to a surface pressure change of approximately 1hPa, a ΔP change of 5‰ is equivalent to a surface pressure change of approximately 5hPa, a ΔP change of 1% is equivalent to a surface pressure change of approximately 1kPa, and a ΔP change of 5% is equivalent to a surface pressure change of approximately 5kPa). Then, subtract the elevation angle errors from the condition of ΔP being 0. Here, it is defined that the difference between the elevation angle error under the condition of ΔP changing 1‰ and the elevation angle error under the condition of ΔP being 0 is err or1‰, the difference between the elevation angle error when ΔP changes by 5‰ and the elevation angle error when ΔP is 0 is error5‰, the difference between the elevation angle error when ΔP changes by 1% and the elevation angle error when ΔP is 0 is error1%, and the difference between the elevation angle error when ΔP changes by 5% and the elevation angle error when ΔP is 0 is error5%. The ranges of error1‰, error5‰, error1%, and error5% for the aircraft in the apparent elevation angle range of 5–30° at flight altitudes of 40km, 70km, and 100km, respectively, are shown in Table 16.

[0162] Table 16 Ranges of error 1‰, error 5‰, error 1%, and error 5% within the apparent elevation angle range (unit: arc seconds)

[0163]

[0164] From Table 16, we can see that as the aircraft altitude increases, the change in elevation angle error caused by pressure decreases. As the aircraft's viewing direction and the deflection angle relative to the vertical line of the earth's center increase, the change in elevation angle error caused by pressure increases. For every 1 kPa change in pressure, the elevation angle error changes by about 10 -3 –10 -2 At the arc second level, for every 5kPa change in pressure, the elevation error changes by 10 -1 At the arc second level, it is found that when the pressure at the location of the object changes by 5 kPa, the impact on the elevation error accuracy is less than 5%.

[0165] (4) The influence of latitude on elevation error

[0166] Elevation angle errors were calculated for representative land areas in the low, mid, and high latitudes of the Northern Hemisphere. The specific information is as follows: East Kalimantan Province, Indonesia (1°N, 115°E) for the low latitude region, Beijing (40°N, 116°E) for the mid-latitude region, and Yakutia, Russia (70°N, 116°E) for the high latitude region. Elevation angle errors were calculated for aircraft at flight altitudes of 40 km, 70 km, and 100 km for apparent elevation angles of 5–30°, as shown in Table 16. In addition to the geographic latitude and longitude, other environmental parameters were: time 12:00:00 UTC, September 1, 2022, solar activity index F107 of 60 sfu, geomagnetic activity index Ap of 10 nT, and wavelength of 0.58 μm. Table 17 shows that the elevation angle error decreases with increasing latitude. This is because in areas with high latitudes, the air pressure is high, the temperature is low, and the air is thin. Compared with areas with medium and low latitudes, the refraction effect is not particularly significant.

[0167] Table 17 Calculation of elevation angle error in low, medium and high latitudes

[0168]

[0169] (5) Seasonal influence on elevation error

[0170] To analyze the seasonal impact of elevation error, the elevation error in the Beijing area was discussed on April 15, 2021 (spring), July 15 (summer), October 15 (autumn), and January 15, 2022 (winter). The elevation error was found to be greatest in winter, smallest in summer, and intermediate in spring and autumn. However, as altitude increased, the elevation error gradually increased in summer and decreased in winter, as shown in Table 18. This is because the atmosphere contracts due to lower temperatures in winter. At lower altitudes, the atmospheric density is greater in winter than in summer, leading to a more pronounced refraction effect. However, as altitude increases, the atmospheric density decreases rapidly in winter relative to summer, causing the elevation error to decrease in winter relative to summer.

[0171] Table 18 Seasonal variation of elevation angle error

[0172]

[0173] Table 19 Comparison of the results of the present invention and SIDNEYBERTRAM

[0174]

[0175] As shown in Table 19, by comparing with the calculation results of SIDNEYBERTRAM, it is found that the maximum relative error between the two is 25.6%, and the minimum relative error is 5.9%. Figure 7 As shown in the comparison chart.

[0176] Difference Analysis:

[0177] Significance of accuracy improvement:

[0178] The error of the present invention in low-altitude areas (1 km) is 13.82 microradians, which is 25.6% higher than that of SIDNEYBERTRAM (11 microradians), but the error is significantly reduced to 5.9% in high-altitude areas (9 km).

[0179] Key advance: The error systematically decreases with increasing altitude (from 25.6% to 5.9%), demonstrating that the invention is more adaptable to the vertical structure of the atmosphere.

[0180] Adaptability to modern atmospheric conditions:

[0181] The SIDNEYBERTRAM model was based on atmospheric data from 1966 and did not take into account the long-term changes in atmospheric parameters caused by the greenhouse effect (such as the global increase in density, temperature, and pressure).

[0182] The present invention dynamically integrates real-time environmental parameters (temperature, pressure, humidity) and a multi-band correction mechanism to better fit the current atmospheric state, and the calculation results reflect the actual physical change trend, such as Figure 7 As shown in the comparison chart.

[0183] Limitations of existing technologies:

[0184] Due to outdated data, the SIDNEYBERTRAM model has an error of up to 25.6% in low-altitude areas, which cannot meet the needs of modern high-precision remote sensing (such as satellite earth observation requires an error of <1%).

[0185] By optimizing the layering strategy (900-1000 layers) and dual-model fusion (Hopfield + e index), the present invention reduces the error to less than 10% in high-altitude areas (>5km), breaking through the accuracy bottleneck of traditional models.

[0186] Innovation of technical effects:

[0187] Error convergence characteristics: The error of the present invention at 9 km (5.9%) is less than a quarter of the error at 1 km (25.6%), highlighting the effect of layered optimization in suppressing cumulative errors.

[0188] Practical application value: Compared with static historical models, this invention supports precise corrections in the context of global warming and provides a reliable data basis for high-altitude remote sensing (such as satellite positioning and disaster monitoring).

[0189] By integrating modern atmospheric parameters with layered optimization, this method significantly reduces the error gap with the classic model (especially at high altitudes), addressing the systematic bias issues associated with outdated data in the Sidneybertram model and providing a more reliable error compensation solution for Earth observation. The construction process incorporates the Hopfield model of atmospheric refractivity and the e-exponential model to simulate the atmospheric refractivity profile. Ultimately, by calculating the difference between the aircraft's apparent elevation angle and its true elevation angle, an elevation error model is constructed. This model corrects for elevation errors caused by atmospheric refraction, enabling precise identification and positioning of observed targets.

[0190] Example 2:

[0191] Based on Example 1, the ground object detection refraction error compensation modeling system of the present invention includes:

[0192] Layering module: used to divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers;

[0193] Refraction angle calculation module: Iteratively solves the refraction angle of each atmospheric layer based on Snell's law;

[0194] Horizontal distance calculation module: calculates the horizontal distance between adjacent layers based on the refraction angle and layer distance;

[0195] Projection distance module: accumulates the horizontal distances of all layers to obtain the distance from the projection of the aircraft on the surface to the true position of the ground object;

[0196] True elevation angle calculation module: combines the vertical distance of the aircraft and the projected distance to calculate the true elevation angle;

[0197] Error calculation module: Calculates the elevation angle error and distance error based on the difference between the true elevation angle and the apparent elevation angle.

[0198] The value of N in the layered module ranges from 900 to 1000, and the distance between adjacent layers is fixed at 100 meters.

[0199] It can correct the elevation angle error and distance error of the aircraft caused by atmospheric refraction, and thus be used for accurate identification and positioning of the observed target.

[0200] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A ground object detection refraction error compensation modeling method, characterized in that: The steps include: S1: Divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers; S2: Solve the angle of refraction of light at each atmospheric layer according to Snell's law; S3: Calculate the horizontal distance between two adjacent atmospheric layers along the light propagation path; S4: Based on the result of step S3, the distance between the projection of the aircraft on the ground surface and the true position of the ground object is calculated; S5: combining the vertical distance from the aircraft to the earth's surface and the distance obtained in step S4, calculating the angle between the line connecting the aircraft and the true position of the ground object and the vertical line to the center of the earth, i.e., the true elevation angle; S6: According to the true elevation angle of step S5 and the angle between the line connecting the aircraft to the ground object and the vertical line of the center of the earth, ie, the apparent elevation angle, calculate the elevation error and distance error; When the atmosphere is divided into N layers in step S1, the distance between two adjacent layers is ,in h is the distance from the aircraft to the Earth's surface; In step S2, the Earth's atmosphere is layered. Assuming that the atmospheric density is the same within the same layer and different between different layers, then Snell's law is satisfied between two adjacent layers. Similarly, the following relationship holds true: From this, the refraction angle of each layer can be calculated: in: is the refractive index of the 0th layer of atmosphere, is the incident angle of layer 0, is the refractive index of the first layer of atmosphere, is the refraction angle of the first layer, and so on. is the refractive index of the N-1th layer of atmosphere, is the incident angle of the N-1th layer, is the atmospheric refractive index of the Nth layer, is the refraction angle of the Nth layer; according to the interior alternate angle theorem, the calculated refraction angle is the incident angle of the next layer; The calculation of the atmospheric refractive index includes: The atmospheric refractive index at the apparent position of the ground object is expressed by the following formula: Where, , t, P, e a ,λ They refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the apparent location of the object, respectively; The atmospheric refractive index along the light propagation path is expressed by the following formula: in, Indicates elevation, by 40136+148.72× t Calculated, the unit is m, below the elevation, each altitude position The atmospheric refractive index at the altitude is given by the Hopfield model. Above the altitude, the altitude The atmospheric refractive index at e The exponential model is given by represents the atmospheric refractive index at the altitude, β is the piecewise fit index.

2. The ground object detection refraction error compensation modeling method according to claim 1, characterized in that: The horizontal distance between two adjacent layers in step S3 is calculated using the following formula: 。 3. The ground object detection refraction error compensation modeling method according to claim 1, characterized in that: In step S4, the distance between the projection of the aircraft on the ground and the true position of the ground object is calculated based on the result obtained in step S3. : 。 4. The ground object detection refraction error compensation modeling method according to claim 3, characterized in that: In step S6, the actual elevation angle calculated in step S5 is combined with the angle between the line connecting the aircraft and the apparent position of the ground object and the vertical line to the center of the earth, that is, the apparent elevation angle, to calculate the elevation angle error, which is expressed as: Among them, Z0 is the angle between the line connecting the aircraft and the ground object and the vertical line of the center of the earth, that is, the apparent elevation angle. This value is a known quantity. θ It is the angle between the line connecting the true position of the aircraft and the ground object and the vertical line to the center of the earth, that is, the true elevation angle, which is calculated in step S5.

5. The ground object detection refraction error compensation modeling method according to claim 4, characterized in that: The distance error in step S6 represents the distance between the true position of the object and the apparent position of the object, and is expressed as It is expressed as follows: in, h is the distance from the aircraft to the surface of the earth, which is a known quantity. It is the distance from the projection of the aircraft on the surface of the earth to the true position of the object. Z0 is the angle between the line connecting the apparent position of the aircraft and the object and the vertical line to the center of the earth, that is, the apparent elevation angle.

6. A ground object detection refraction error compensation modeling system, based on the ground object detection refraction error compensation modeling method according to any one of claims 1 to 5, characterized in that: include: Layering module: used to divide the atmosphere between the aircraft and the ground into N layers and calculate the distance between two adjacent layers; Refraction angle calculation module: Iteratively solves the refraction angle of each atmospheric layer based on Snell's law; Horizontal distance calculation module: calculates the horizontal distance between adjacent layers based on the refraction angle and layer distance; Projection distance module: accumulates the horizontal distances of all layers to obtain the distance from the projection of the aircraft on the surface to the true position of the ground object; True elevation angle calculation module: combines the vertical distance of the aircraft and the projected distance to calculate the true elevation angle; Error calculation module: Calculates the elevation angle error and distance error based on the difference between the true elevation angle and the apparent elevation angle.

7. The ground object detection refraction error compensation modeling system according to claim 6, characterized in that: The value range of N in the layered module is 900 to 1000, and the distance between adjacent layers is fixed at 100 meters.

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